It is known that the generic n-th order moment (n being an integer and positive number) of the electromagnetic field of an optical beam is given by the relation: ##EQU1## where I(r) is the near field or far field beam intensity at a distance r from the axis.
More particularly, the square root W.sub.0 of the 2nd order moment, i.e. the root mean square of the spatial distribution of the electromagnetic field of the beam (or of the field at the output of an optical fiber, in the preferred application) represents the beam spot-size.
The knowledge of W.sub.0 is important for the knowledge of the geometric dimensions of the field, which gives information both as to the collimation of and as to the power distribution in the beam.
In the particular case of optical fibers (to which reference will be made hereinafter since the invention has been mainly developed for applications in that domain), spot-size data provides information on propagation within the fiber and on splice losses; such information is indispensable when using optical fibers in a telecommunications system. Even more particularly, spot-size W.sub.0 both in the near and in the far field characterizes the properties of monomode fibers; in fact for such fibers splice and bending losses, and cabling losses due to microbending, can be obtained from these parameters. The variation of spot-size with wavelength indicates the cut off wavelength of the first higher order mode, as well as the fiber dispersion.
A number of different techniques have been proposed for spot-size measurements in optical fibers.
One is described by R. Yamauchi, T. Murayama, Y. Kikuchi, Y. Sugawara and K. Inada in the paper "Spot-Sizes of Single Mode Fibres With a Noncircular Core" presented at the Fourth International Conference on Integrated Optics and Optical Fibre Communication (IOOC'83, Tokyo, Japan, June 27-30, 1983, Paper 28A2-3, pages 39 and ff.). In this method, spot size is obtained by determining the value of I at the fiber output by near field intensity scanning and then by directly applying relation (1), with n=2. This method can be used for measuring moments of any order. Since the integration interval extends to infinity, but, beyond a certain distance from the beam axis, intensity I will be masked by measurement noise, the method can introduce some significant errors into the value obtained. In addition, radial scanning is inherently complex.
According to other methods a Gaussian distribution is assumed for the function representing I and quantities are measured which can be correlated to spot size by means of formulae, which are valid only if the hypothesis of a Gaussian field is satisfied. Examples of such methods are described in the papers: "Direct Method of Determining Equivalent-Step-Index Profiles for Multimode Fibres" by C. A. Millar, Electronics Letters, Vol. 17, No. 13, June 25, 1981, pp. 458 and ff., and "Fundamental Mode Spot-Size Measurement in Single-Mode Optical Fibres" by F. Alard, L. Jeunhomme, P. Sansonetti, Electronics Letters, Vol. 17, N. 25, Dec. 10, 1981, pp. 958 and ff. Since the hypothesis of Gaussian field applies only in very particular cases, the measurements obtained by these methods present an intrinsic uncertainty which is difficult to quantify.